Hector Permafrost
Alexey N. Shiklomanov
Ben Bond-Lamberty
Ben Kravitz
Corinne Hartin
23 January, 2020
Abstract
Text of abstract
## Loading hector1 Introduction
Climate change is a problem (IPCC, 2013). Important to reduce carbon emissions to meet temperature targets. The extent of anthropogenic emissions reduction depends on what how much help (or push-back) we get from the physical and biological Earth systems.
Permafrost is an important C reservoir. The total northern soil C pool is estimated at 1672 PgC, of which approximately 1466 Pg (88%) is in permafrost (Tarnocai et al., 2009). More recent estimates suggest that total high-latitude soil organic matter pool is 1300 Pg, with roughly 800 Pg in permafrost (Hugelius et al., 2014). This frozen C can be released into the atmosphere by several processes related to warming, including aerobic respiration in thawed soil (REF) and anaeribic respiration in thermokarst lakes and wetlands (Turetsky et al., 2002; Wickland et al., 2006). But emissions from wet soils may be offset by high organic matter accumulation rates (Camill et al., 2001). Permafrost thaw in boreal peatlands in north-central Saskatchewan increased CO2 and CH4 fluxes from soil to atmosphere by 1.6 and 30 times, respectively (Turetsky et al., 2002). These impacts are exacerbated by the fact that the Arctic is warming roughly 2.5 (TODO ???) times faster than the global average (TODO REF). Projections of permafrost C emissions vary. (Schuur et al., 2009) estimate 0.8 - 1.1 Pg C yr-1. Back-of-the-envelope estimates from (Zimov et al., 2006): 10-40 g C m-3 day-1 off the bat, slowing down to equilibrium (?) rate of 0.5-5 g C m-3 day-1 for several years.
Rapid methane release from arctic permafrost could potentially cause trillions in economic damage (Whiteman et al., 2013).
On the other hand, warming and CO2 fertilization may increase vegetation productivity, which could increase soil C storage through enhanced litterfall; the balance of these two processes is uncertain (Jones et al., 2005). There are additional uncertainties associated with vegetation composition (spatially variable peat accumulation) (Camill et al., 2001). Other large uncertainties related to soil properties and climate model structure (Harp et al., 2016). Several modeling studies generally predict increases in soil C sequestration at high latitudes (Burke et al., 2017; Ito et al., 2016; Qian et al., 2010). However, this increase is dampened or even reversed when C emissions from permafrost thaw are included (Burke et al., 2017; Schaefer et al., 2011).
The importance of Arctic climate feedbacks has led to efforts to incorporate these processes—particularly, permafrost thaw—into land surface models. Early efforts derived permafrost extent and C based purely on soil temperature (Lawrence and Slater, 2005). (More recent models have done this better…) Schaefer et al. (2011) – SiBCASA estimates 190 +/- 64 Gt C, but this does not include warming feedback or discontinuous permafrost regions. Harp et al. (2016) – Community Earth System Model (CESM) simulations over 100 years. (Burke et al., 2017) – JULES and ORCHIDEE, with new permafrost scheme, combined with intermediate complexity climate-ocean model (IMOGEN), to look at climate sensitivity to permafrost C emissions. Models are highly sensitive to representation of soil processes, which can be more important than differences in scenario and/or climate drivers (Burke et al., 2017). But Harp et al. (2016) argue that model structural uncertainty is larger than soil property uncertainty.
Land surface models are expensive to run, making it challening to use them for uncertainty quantification and exploration of alternative policy scenarios. Simple climate models are an alternative. (More on simple climate models).
(Previous attempts to incorporate permafrost into simple climate models.)
Hector (Hartin et al., 2015). In this study, we use Hector to evaluate the global sensitivty of climate to terrestrial biosphere processes, and how this uncertainty is affected by permafrost emissions. The current version of Hector does not have an explicit representation of permafrost C emissions. In this study, we investigate whether the additional complexity and parametric and structural uncertainty of an explicit representation of permafrost may be warranted in Hector. To do this, we evaluate the sensitivity of climate variables (as predicted by Hector) to several different exogenous scenarios of permafrost C emissions. (TODO Modify this to be about economic impact)
Some more relevant references: - (Zimov et al., 2006) - (Treat and Frolking, 2013) - (Burke et al., 2017; Drake et al., 2015; Hope and Schaefer, 2015; Kessler, 2017; Kuhry et al., 2010; Lee et al., 2011; Schaefer et al., 2014, 2011; Schuur and Abbott, 2011; Schuur et al., 2015)
2 Methods
2.1 Model description: Hector
Hector (Hartin et al., 2015, p.@hartin_2016_ocean,). Simple climate model.
(TODO: More details on terrestrial C cycle in Hector). The default heterotrophic respiration (\(R\)) scheme for a pool \(p\) (detritus or soil) in Hector:
\[ R_{p} = C_p \times f_p \times Q_{10} ^ \frac{T}{10} \]
2.2 Hector permafrost sub-model
The general principle is that permafrost constitutes an additional reserve of soil carbon that, because it is frozen, is inaccessible to microbes. As permafrost thaws and some fraction of this carbon becomes accessible to microbes, it is transferred from the frozen permafrost pool to the standard soil C pool, where it is decomposed by Hector’s standard decomposition routine. Let \(C_{pf}[t]\) be the permafrost C pool and \(C_{s}[t]\) be the soil C pool at time \(t\) (both in units of Pg C), and let \(\Delta C_{pf}[t]\) be the change in the permafrost C pool at time \(t\). The C consequences of permafrost thaw can therefore be represented as:
\[ C_{pf}[t] = C_{pf}[t-1] - \Delta C_{pf}[t] \]
\[ C_{s}[t] = C_{s}[t] + \Delta C_{pf}[t] \]
Let \(C[0]_{pf}\) be the initial size of the permafrost C pool (Pg C) and \(\Phi[t]\) be the fraction of permafrost remaining (in arbitrary area or volume units) at time \(t\). Assuming a uniform permafrost C density, \(\Delta C_{pf}[t]\) can be expressed as:
\[ \Delta C_{pf}[t] = \Delta \Phi[t] C_{pf}[t-1] \]
To a first approximation, \(\Phi[t]\) is a function of air temperature (\(T[t]_{air}\)). Kessler (2015) assume this relationship is linear. However, because the permafrost area fraction is, by definition, bounded by zero (and 11), and because deeper permafrost thaws more slowly than shallow permafrost, we use a negative logistic relationship instead:
\[ \Phi[t] = 1 - \left( 1 + a \exp\left( b * T_{air}[t] \right) \right) ^ c \]
where \(a\), \(b\), and \(c\) are model parameters. The change in frozen fraction at a given time step, \(\Delta \Phi[t]\), is given by:
\[ \Delta \Phi[t] = \max(\Phi[t] - \Phi[t-1], 0) \]
In other words, permafrost thaw is permanent – once it thaws, it does not re-freeze, even if the temperature drops.
For globally-averaged permafrost, \(a = 2.371\), \(b = -0.676\), and \(c = -3.685\) to most closely reproduce the rate of 0.172 K\(^{-1}\) reported by Kessler (2015) over the range of 0.82 to 4 K above the pre-industrial baseline.
Figure 1: Fraction of permafrost thaw as a function of change in global annual mean air temperature since pre-industrial (1750).
2.3 Configuration
Initial permafrost C is set to 1035 Pg C.
3 Results
3.1 Effect of permafrost C
Figure 2: Effect of permafrost C emissions on scenarios.
4 Discussion
Rate of permafrost C release also depends on soil moisture conditions – drier soils release C much faster (“carbon bomb”) than wetter soils (“carbon fizz”) (Elberling et al., 2013). Moisture will also affect the balance of aerobic (CO2 release) vs. anaerobic (CH4) C release (Turetsky et al., 2002), to the extent that unclear if anaerobic (wet) areas are C sources or sinks (Wickland et al., 2006). Effects of permafrost thaw on soil moisture are a complex hydrological problem – drainage very sensitive to local (micro-)topography (Wickland et al., 2006). So will vegetation cover (Wickland et al., 2006).
Temperature amplification of permafrost carbon feedback (by 2100) 0.02 to 0.36 °C (Burke et al., 2013; Schneider von Deimling et al., 2015, 2012), or 0.1 to 0.8 °C in (MacDougall et al., 2012, 2013), or 10-40% of peak temperature change (Crichton et al., 2016), or 0.2 to 12% (Burke et al., 2017).
Permafrost carbon has greater impact at lower emissions scenarios (Burke et al., 2017; MacDougall et al., 2012, 2013) .
5 Conclusion
6 Acknowledgments
Funded by EPA grant XXX. Cyberinfrastructure support from Pacific Northwest National Laboratory (PNNL).
7 Miscellaneous notes
7.1 Permafrost emissions scenarios
Digitized scenarios from (Schaefer et al., 2011).
SiBCASA model predictions of CO2 emissions (permafrost respiration; \(R_{pc}\); note – no methane!) through 2300.
These results were digitized using WebPlotDigitizer (https://apps.automeris.io/wpd/), and interpolated to annual resolution (using R stats::spline function).
Digitized scenarios from (Hope and Schaefer, 2015). CO2 and CH4 emissions from SiBCASA model.
(Schuur et al., 2009) – Estimate 0.8 - 1.1 Pg C yr-1.
Back-of-the-envelope estimates from (Zimov et al., 2006): - 500 Gt C in loess that could be completely emitted by 2100 (plus other C sources). - 10-40 g C m-3 day-1 off the bat, slowing down to equilibrium (?) rate of 0.5-5 g C m-3 day-1 for several years. Combine with data on permafrost spatial extent, density, etc. to generate estimates (but can back-calculate from 500 Gt C above?)
7.2 Parameter calibration
We used the BayesianTools R package (Hartig et al., 2019) for all parameter calibration.
The outputs of these calibrations are joint posterior distributions of parameters and their covariances, from which we sample for the sensitivity analysis.
For global parameters, we used the following likelihood:
\[ \log(L) = \sum_s Normal(Hector(\beta, Q_{10}, s) | CMIP5(s), \sigma) \]
where \(s\) is one of the four representative carbon pathways (RCPs), \(CMIP5(s)\) are the CMIP5 global mean outputs for the corresponding variables, and \(\sigma\) is the model error (estimated during the fit). We also used the resulting distributions for \(\beta\) and \(Q_{10}\) for the non-permafrost biome in cases 2 and 3. We feel this is appropriate because the CMIP5 models against which these parameters are calibrated do not include permafrost C feedbacks.
For case 2, we calibrated the permafrost-specific \(\beta\) and \(Q_{10}\) against various literature sources, including:
- Land surface model simulations (Burke et al., 2017; Hope and Schaefer, 2015; Schaefer et al., 2011).
- Try to calibrate against NPP and soil respiration if possible
- Literature surveys (Schaefer et al., 2014)
- Warming experiments (Wickland et al., 2006)
- TODO: Others?
Some of these are time series, while others are individual estimates at particular points in time. To give them equal weight in the likelihood, we down-weight the time series likelihoods by the number of time steps.
We derived a distribution for the Arctic warming factor from TODO.
TODO: Table and multi-panel figure of input datasets.
For the \(\alpha\) and \(\phi\) parameters in case 3, we looked at the literature on permafrost methane emissions (e.g., Wickland et al., 2006).
7.3 Other notes
Frozen carbon residence time (FCRt) from (Burke et al., 2017):
\[ FCRt = FCRt0 * exp(-\Delta T / \Gamma) (for \Delta T > 0.2 °C) \]
- \(FCRt_0\) (years) reflects the stability of permafrost C (length of time that permafrost C is stable when \(\Delta T = 0\))
- \(\Gamma\) – decay term (°C); temperature change at which “the number of years taken for all of the old permafrost C to be emitted reduces to 1/e of its initial value”
Other Hector parameters to consider.
| Variable | INI name | Description | Value |
|---|---|---|---|
| \(f_{nv}\) | f_nppv |
Fraction of NPP C transferred to vegetation | 0.35 |
| \(f_{nd}\) | f_nppd |
Fraction of NPP C transferred to detritus | 0.60 |
| \(f_{nd}\) | Fraction of NPP C transferred to soil | 0.05 | |
| \(f_{lv}\) | f_lucv |
Fraction of LUC change flux from vegetation | 0.10 |
| \(f_{ld}\) | f_lucd |
Fraction of LUC change flux from detritus | 0.01 |
| \(f_{ls}\) | Fraction of LUC change flux from soil | 0.89 | |
| \(f_{ds}\) | Fraction of detritus C that goes to soil | 0.60 | |
| \(f_{rd}\) | Fraction of respiration C to detritus | 0.25 | |
| \(f_{rs}\) | Fraction of respriation C to soil | 0.02 |
According to (Hartin et al., 2015), these were selected to be “generally consistent with previous simple earth system models (e.g., Meinshausen et al., 2011)”.
7.3.0.0.1 pagebreak
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9 Appendix
Figure 3: Figure 1: Input parameter distributions for global Hector.
Figure 4: Figure 2: Input parameter distributions for Hector with biomes.
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#> Local: master /Users/shik544/Projects/hector_project/permafrost_emit
#> Head: [4189215] 2020-01-23: Show permafrost frozen fraction outputTechnically, permafrost area could increase in the case of cooling temperatures, and therefore the area fraction could be greater than 1. However, because even the most aggressive climate action scenarios show temperatures that stabilize above year 2000, we assume that permafrost area will never grow more than the starting value.↩︎
Kessler (2015) report this as temperature change from year 2000. 0.8 K is the warming since pre-industrial as estimated by the default Hector configuration.↩︎